Late Wednesday evening, Southwest sent out an updated statement acknowledging that hundreds of flights had been cancelled and that it may take a few days for things to get back to normal.

"Southwest Airlines is reducing the number of flights departing Southwest.com and plan to arrive to the airport early, as longer than typical lines are likely," the statement read. "Our Teams are working diligently through the night to resolve issues as quickly as possible."

Southwest said it began experiencing intermittent performance issues earlier with multiple technology systems as a result of an outage.

"Flight delays across our network have resulted in 600-700 canceled and delayed flights," the statement said. "Systems are gradually coming back online and we continue to move toward a normal operation. We sincerely apologize to our Customers whose travel plans have been impacted."

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Leah Boyd and her husband, Matt, were flying to Providence, Rhode Island, but were held up at the Baltimore airport for three hours by mechanical issues with two different planes.

They finally boarded a plane, but after sitting at the gate for nearly an hour passengers were asked to exit because of the technology outage, Boyd said.

Then the pilots reached the end of their shifts, so passengers waited for a replacement crew. The Boyds ended up canceling their reservations and planned to drive to Providence on Thursday instead.

Leah figured it would be hard to find seats on another flight. "I've never seen so many people in the terminal," she said. "All these people are going to be flying standby."

Anxious customers tweeted to Southwest that they could not check in for flights. The airline's website wasn't working normally -- visitors couldn't buy tickets, check in for flights, or check their flight's status.

Airlines have sprawling, overlapping and complicated technology systems, and even brief outages can cause thousands of passengers to be stranded for hours.

Stranded passengers at the New Orleans Airport after a Southwest Airlines computer outage caused massive delays.

Peter King/CBS News

Last October, an outage caused about 800 Southwest flights to be delayed and forced employees to issue tickets and boarding passes by hand. The airline blamed a software application, and it recovered in about a day. United Airlines and American Airlines both had computer problems last summer but fixed the problems within a day.

Dallas-based Southwest Airlines Co. carries more passengers within the United States than any airline. However, it is far smaller than American, Delta and United when international traffic is included.